Component Selection Distance
There is currently no setting for this. You can see in the Interface tab of the user preferences menu that there's a 'hotspot' distance for the handles of manipulators and similar settings for Pie menus. This is probably where you'd expect to find such a setting and it isn't exposed there.



Maybe more substantially, in this mirror of the Blender source code on line 446 a comment mentions that the below function uses a hardcoded value (line 392) of 5px for unselected vertices. This isn't necessarily the only way to select vertices in Blender but it seems to be the default.